Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditioned matrix. Comparison theorems show that the rate of convergence of the preconditioned Gauss-Seidel method is faster than the preconditioned mixed-type splitting and AOR (SOR) iterative methods. Finally, some numerical examples are presented to illustrate the reality of our comparison theorems.
Mohseni Moghadam, M., Panjeh Ali Beik, F. (2012). Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems. Bulletin of the Iranian Mathematical Society, 38(2), 349-367.
MLA
M. Mohseni Moghadam; Fatemeh Panjeh Ali Beik. "Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems". Bulletin of the Iranian Mathematical Society, 38, 2, 2012, 349-367.
HARVARD
Mohseni Moghadam, M., Panjeh Ali Beik, F. (2012). 'Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems', Bulletin of the Iranian Mathematical Society, 38(2), pp. 349-367.
VANCOUVER
Mohseni Moghadam, M., Panjeh Ali Beik, F. Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems. Bulletin of the Iranian Mathematical Society, 2012; 38(2): 349-367.
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